jobshop.ppt - Introduction to Job Shop Scheduling Problem...

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Introduction to Job Shop Scheduling Problem Qianjun Xu Oct. 30, 2001
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Description of Job Shop Scheduling A finite set of n jobs Each job consists of a chain of operations A finite set of m machines Each machine can handle at most one operation at a time Each operation needs to be processed during an uninterrupted period of a given length on a given machine Purpose is to find a schedule, that is, an allocation of the operations to time intervals to machines, that has minimal length
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Formal Definition of JSS Job set Machine set Operations Each operation has processing time On O define A, a binary relation represent a precedence between operations. If then v has to be performed before w. A induce the total ordering belonging to the same job; no precedence exist between operations of different jobs. } ... , , { 2 1 n j j j J } ... , , { 2 1 m m m m M } ,... , { 2 1 i im i i i o o o O } ,... , { 2 1 i im i i } ... , , { 2 1 n o o o O A w v ) , (
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Formal Definition of JSS cont. A schedule is a function that for each operation v defines a start time S(v). A schedule S is feasible if The length of a schedule S is The goal is to find an optimal schedule, a feasible schedule of minimum length., min(len(S)).
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